{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RDJSPQNAMYDC6YVAKZH26XTW6L","short_pith_number":"pith:RDJSPQNA","canonical_record":{"source":{"id":"2606.18752","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-17T06:56:55Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"title_canon_sha256":"95ff6849d1b72ef30ad9cda0d85454d438d404a0195b5abbf93ffaa09b0a5bf4","abstract_canon_sha256":"a2fd052be84783e84ac700bd5b47b0bdefc67b6bf63db8e6e0ed67dd6564fc9d"},"schema_version":"1.0"},"canonical_sha256":"88d327c1a066062f62a0564faf5e76f2e271e926290853f048e2120d625a3e6d","source":{"kind":"arxiv","id":"2606.18752","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18752","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18752v2","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18752","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"RDJSPQNAMYDC","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"pith_short_16","alias_value":"RDJSPQNAMYDC6YVA","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"pith_short_8","alias_value":"RDJSPQNA","created_at":"2026-06-19T16:12:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RDJSPQNAMYDC6YVAKZH26XTW6L","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18752","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-17T06:56:55Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"title_canon_sha256":"95ff6849d1b72ef30ad9cda0d85454d438d404a0195b5abbf93ffaa09b0a5bf4","abstract_canon_sha256":"a2fd052be84783e84ac700bd5b47b0bdefc67b6bf63db8e6e0ed67dd6564fc9d"},"schema_version":"1.0"},"canonical_sha256":"88d327c1a066062f62a0564faf5e76f2e271e926290853f048e2120d625a3e6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:58.344099Z","signature_b64":"pEatr6j/3mrnH+dqj/xuTqanTX7sfSNT1Lp52BBl3Bt+3C4519AFYE25ufypzInWDrZomDwYJWDqFThLL/K1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88d327c1a066062f62a0564faf5e76f2e271e926290853f048e2120d625a3e6d","last_reissued_at":"2026-06-19T16:12:58.343727Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:58.343727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18752","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"azpZMyt7dMaI7NgnSMvfAr14+CFvLqIcYgWsoSFW5GEIxslNZqqnzvnTACwnx2vprQHKx7UXGfPzZLT+9PflBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:08:31.692948Z"},"content_sha256":"c40e544e68b9ea1864bc138c22e953e39d46d4c08e3e3134daf6d456fba80d8d","schema_version":"1.0","event_id":"sha256:c40e544e68b9ea1864bc138c22e953e39d46d4c08e3e3134daf6d456fba80d8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RDJSPQNAMYDC6YVAKZH26XTW6L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"C. Itoi, Y. Sakamoto","submitted_at":"2026-06-17T06:56:55Z","abstract_excerpt":"The self-averaging of the replica overlap is proven in the Edwards-Anderson (EA) model under random field almost everywhere in the coupling constant space in any dimension. The EA order parameter is represented in terms of the derivative of the free energy density with respect to the random field strength, regardless of boundary conditions. Tasaki's correlation inequality for finite-dimensional spin glass models shows that the expectation of the squared replica overlap is bounded by the squared EA order parameter. These simple evaluations enable us to prove that the variance of the replica ove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18752","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18752/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6vc8iwXL1nQhpZ9NzfdrHgG6XQLZPzWQFo0mOliPk3vQe37QrLwmtYvgmGEm5bY12Ox/Phx0rhVISWCXbkmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:08:31.693343Z"},"content_sha256":"3ae04ed3214afa5313b03cdbb8c9bb1f06fa84a58cfdb4992771cb7af7c60dc9","schema_version":"1.0","event_id":"sha256:3ae04ed3214afa5313b03cdbb8c9bb1f06fa84a58cfdb4992771cb7af7c60dc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDJSPQNAMYDC6YVAKZH26XTW6L/bundle.json","state_url":"https://pith.science/pith/RDJSPQNAMYDC6YVAKZH26XTW6L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDJSPQNAMYDC6YVAKZH26XTW6L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T00:08:31Z","links":{"resolver":"https://pith.science/pith/RDJSPQNAMYDC6YVAKZH26XTW6L","bundle":"https://pith.science/pith/RDJSPQNAMYDC6YVAKZH26XTW6L/bundle.json","state":"https://pith.science/pith/RDJSPQNAMYDC6YVAKZH26XTW6L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDJSPQNAMYDC6YVAKZH26XTW6L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RDJSPQNAMYDC6YVAKZH26XTW6L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a2fd052be84783e84ac700bd5b47b0bdefc67b6bf63db8e6e0ed67dd6564fc9d","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-17T06:56:55Z","title_canon_sha256":"95ff6849d1b72ef30ad9cda0d85454d438d404a0195b5abbf93ffaa09b0a5bf4"},"schema_version":"1.0","source":{"id":"2606.18752","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18752","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18752v2","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18752","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"RDJSPQNAMYDC","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"pith_short_16","alias_value":"RDJSPQNAMYDC6YVA","created_at":"2026-06-19T16:12:58Z"},{"alias_kind":"pith_short_8","alias_value":"RDJSPQNA","created_at":"2026-06-19T16:12:58Z"}],"graph_snapshots":[{"event_id":"sha256:3ae04ed3214afa5313b03cdbb8c9bb1f06fa84a58cfdb4992771cb7af7c60dc9","target":"graph","created_at":"2026-06-19T16:12:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.18752/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The self-averaging of the replica overlap is proven in the Edwards-Anderson (EA) model under random field almost everywhere in the coupling constant space in any dimension. The EA order parameter is represented in terms of the derivative of the free energy density with respect to the random field strength, regardless of boundary conditions. Tasaki's correlation inequality for finite-dimensional spin glass models shows that the expectation of the squared replica overlap is bounded by the squared EA order parameter. These simple evaluations enable us to prove that the variance of the replica ove","authors_text":"C. Itoi, Y. Sakamoto","cross_cats":["cond-mat.dis-nn","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-17T06:56:55Z","title":"Self-averaging of replica overlaps in the random field Edwards-Anderson model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18752","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c40e544e68b9ea1864bc138c22e953e39d46d4c08e3e3134daf6d456fba80d8d","target":"record","created_at":"2026-06-19T16:12:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a2fd052be84783e84ac700bd5b47b0bdefc67b6bf63db8e6e0ed67dd6564fc9d","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-17T06:56:55Z","title_canon_sha256":"95ff6849d1b72ef30ad9cda0d85454d438d404a0195b5abbf93ffaa09b0a5bf4"},"schema_version":"1.0","source":{"id":"2606.18752","kind":"arxiv","version":2}},"canonical_sha256":"88d327c1a066062f62a0564faf5e76f2e271e926290853f048e2120d625a3e6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88d327c1a066062f62a0564faf5e76f2e271e926290853f048e2120d625a3e6d","first_computed_at":"2026-06-19T16:12:58.343727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:58.343727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pEatr6j/3mrnH+dqj/xuTqanTX7sfSNT1Lp52BBl3Bt+3C4519AFYE25ufypzInWDrZomDwYJWDqFThLL/K1AQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:58.344099Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18752","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c40e544e68b9ea1864bc138c22e953e39d46d4c08e3e3134daf6d456fba80d8d","sha256:3ae04ed3214afa5313b03cdbb8c9bb1f06fa84a58cfdb4992771cb7af7c60dc9"],"state_sha256":"e114a3f5a38d3d41364a7287b117b765e84f8533a371d6dc5911c988ee621b42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lm+EU2G3tkREwg1tTv7QNJVkfXibn0nM8c+I+GCL1mK0+z8zO122HkwnxZEcd6ecmElhmNDbYsBWkka+U13mCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T00:08:31.695386Z","bundle_sha256":"2583c448fd4e1fe39aa61f98361aa8e174025644bbd56aafa102f69cf5c34e5f"}}